Question

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food − piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.

Answer 1

a) Radius (r) of semi-circular part = `(2.8/2)` cm = 1.4 cm

Perimeter of the given figure = 2.8 cm + πr

= 2.8 cm + `(22/7 xx 1.4)` cm

= 2.8 cm + 4.4 cm

= 7.2 cm

b) Radius (r) of semi-circular part = `(2.8/2)` cm = 1.4 cm

Perimeter of the given figure = 1.5 cm + 2.8 cm + 1.5 cm +π (1.4 cm)

= 5.8 cm + `22/7` (1.4 cm)

= 5.8 cm + 4.4 cm

= 10.2 cm

c) Radius (r) of semi-circular part = `(2.8/2)` cm = 1.4 cm

Perimeter of the figure(c) = 2 cm + πr + 2 cm

= `4 cm + 22/7 xx (1.4 cm)`

= 4 cm + 4.4 cm

= 8.4 cm

Thus, the ant will have to take a longer round for the food-piece (b), because the perimeter of the figure given in alternative (b) is the greatest among all.